Paqueta had been linked with a £70 million ($89m) move to Manchester City recently, but that transfer has since collapsed due to the allegations. According to the Daily Mail, the FA are currently looking into the Brazilian's betting activity.
Although the specifics of the investigation have not been disclosed, it is understood that the alleged breaches relate to gambling on football.
The news will worry West Ham after Brentford forward Ivan Toney was hit with an eight-month ban after admitting to over 200 breaches of the FA's betting regulations. Paqueta arrived from Lyon in August 2022 and impressed in the second half of last season following an inauspicious start, helping David Moyes' side win the Europa Conference League.
City had been considering the midfielder as a replacement for Kevin De Bruyne, who is expected to miss a sizeable chunk of the season after sustaining a hamstring injury during the Cityzens' Premier League curtain raiser against Burnley.
However, it was reported on Friday morning that they had pulled out of negotiations. City are now thought to be considering signing Eberechi Eze from Crystal Palace.
Paqueta started West Ham's season opener against Bournemouth last weekend, but it remains to be seen if he will feature when the Hammers take on Chelsea at the London Stadium on Sunday.